# General Form of Sine Function

The general form of a sine function is: y = sin (Bx-C) + D.

Where:

Amplitude: = |A|. The amplitude is the magnitude of the stretch or compression of the
function from its parent function: y = sin x.

Period: = 2π/B. The period of a trigonometric function is the horizontal distance over which the curve travels before it begins to repeat itself (i.e., begins a new cycle). For a sine or cosine function, this is the length of one complete wave; it can be measured from peak to peak or from trough to trough. Note that 2π is the period of y = sin x.

Phase Shift: = C/B. The phase shift is the distance of the horizontal translation of the
function. Note that the value of in the general form has a minus sign in front of it, just like it does in the vertex form of a quadratic equation: y = (x-h)2+k. So,

• A minus sign in front of the implies a translation to the right, and
• A plus sign in front of the implies a implies a translation to the left.

Vertical Shift: = D. This is the distance of the vertical translation of the function. This is
equivalent to k in the vertex form of a quadratic equation: y = (x-h)2+k.

The General Equation for sine function: could be rewritten as

y = Amplitude . Sin[(360/period)(x-phase shift)] + vertical shift working in degrees

y = Amplitude . Sin[(2π /period)(x-phase shift)] + vertical shift working in radians

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